Homework Help Overview
The discussion revolves around proving two logarithmic properties: the first property relates to the expression ln(b^(1/n)) and its equivalence to (1/n)ln(b) for b>0, while the second property concerns the expression ln(a^r) equating to rln(a) for any rational number r and a>0. The original poster expresses confusion regarding the differences in proving these properties compared to previously established logarithmic identities.
Discussion Character
- Conceptual clarification, Problem interpretation, Assumption checking
Approaches and Questions Raised
- The original poster attempts to understand the distinction between proving logarithmic properties for natural numbers versus rational numbers. They question the relevance of setting b=an and express uncertainty about how this aids in the proof. Other participants suggest that the previous proof method may not apply to rational numbers and encourage exploring the implications of defining r as a fraction.
Discussion Status
Some participants have provided insights into the differences in proof requirements for natural versus rational numbers, noting that assumptions made in the natural number case may not hold for rational numbers. The original poster has made progress on part 1 but remains uncertain about part 2, indicating an ongoing exploration of the topic.
Contextual Notes
The original poster has previously proven ln(a^n) = nln(a) for natural numbers and is now tasked with extending this proof to rational numbers. There is a recognition of the need to adapt the approach due to the nature of rational numbers.